Research On Q-rung Orthopair Fuzzy Set Theory And Its Applications

The q-rung orthopair fuzzy set is an important branch of uncertainty theory,which has extensive application background and theoretical basis in management,medicine,economy and many other fields.This paper aims at the problems and challenges in the q-rung orthopair fuzzy set(aggregation operators,information measures,score functions and inequalities),multi-criteria(group and dynamic)decision-making methods and applications(cache placement policy selection and financial risk assessment of new energy vehicle companies),on the basis of a comprehensive analysis of the current research and development status in the field of theory and application,two kinds of q-rung orthopair fuzzy aggregation operators are designed,a new q-rung orthopair fuzzy information measure and score functions are designed,some q-rung orthopair fuzzy inequalities are constructed,and four novel and reasonable multi-criteria decision-making(MCDM)methods are proposed.The specific work of this paper is as follows:(1)Proposal of the modified and unweighted q-rung orthopair fuzzy aggregation operatorsThe framework of modified method for q-rung orthopair fuzzy number is proposed,which can effectively eliminate the counter-intuitive phenomenon and the problem of limited value.In addition,the q-rung orthopair fuzzy weighted averaging(geometric)operator,q-rung orthopair fuzzy Einstein weighted averaging(geometric)operator and q-rung orthopair fuzzy Dombi weighted averaging(geometric)operator based on modified q-rung orthopair fuzzy number are given,and the monotonicity between the membership and the non-membership of the modified aggregation operators are discussed.On the other hand,we propose an unweighted q-rung orthopair fuzzy mean(Uq-ROFM)operator which is not affected by q-rung orthopair fuzzy number and can directly derive reliable integration values.Finally,two kinds of q-rung orthopair fuzzy aggregation operators are applied to the subsequent multi-attribute decision making and inequality construction,respectively.(2)Design of the new q-rung orthopair fuzzy information measure and score functionThe q-rung orthopair fuzzy distance measure,similarity measure,and entropy based on the area difference are established,and the complement technology is incorporated,and the basic framework of the conversion relationship is derived.At the same time,the q-rung orthopair fuzzy distance measure and similarity measure based on the triangle orthocenter is constructed.The above two similarity measures or distance measures can effectively avoid axiom problems and counter-intuitive phenomena.In addition,relying on the above-mentioned two kinds of q-rung orthopair fuzzy distance measure,the corresponding score functions to compare the size of the data to be evaluated are proposed,respectively.Experiments show that they can effectively solve the problems of denominator being 0,parameter selection,excessive comparison and incomparability.(3)Construction of the new q-rung orthopair fuzzy inequalitiesThe theoretical framework of q-rung orthopair fuzzy inequalities based on operations,aggregation operators and equality is systematically constructed,and a number of inequalities based on subtraction,division operations,and unweighted q-rung orthopair fuzzy aggregation operators are firstly constructed.At the same time,an inequality based on the equality definition of q-rung orthopair fuzzy inequality is innovatively established,which greatly enriches q-rung orthopair fuzzy inequality theory.(4)Research on the q-rung orthopair fuzzy multi-criteria decision-making methods based on TAOV and CoCoSoTwo q-rung orthopair fuzzy MCDM methods with different routes are proposed,which can effectively solve the counter-intuitive problem caused by parameter selection and aggregation operator,the illegal decision mechanism caused by special data and the phenomenon of low differentiation of related decision-making results.On the one hand,q-rung orthopair fuzzy MCDM method based on TAOV(Total Area based on Orthogonal Vectors)not only integrates the combined weight of the decision maker’s subjective and objective preferences,but the correlation between attributes is also considered.On the other hand,q-rung orthopair fuzzy MCDM method based on CoCoSo(Combined Compromise Solution)introduces CRITIC(Criteria Importance Through Inter-criteria Correlation)technology and amplification factor mechanism.Experiments show that the above two kinds of MCDM methods have good effects in the decision-making process,and effectively avoid the above-mentioned shortcomings.(5)Research on the q-rung orthopair fuzzy multi-criteria dynamic decision-making method based on PRSRVThe objective weight determination method based on water-filling theory and the combined weight determination method of nonlinear combined subjective weight and objective weight are proposed,and a q-rung orthopair fuzzy PRSRV(Projection Ranking by Similarity to Referencing Vector)multi-criteria dynamic decision-making framework system with unknown objective weight and combination weight is established.In the early stage of this method,the newly constructed dynamic q-rung orthopair fuzzy aggregation operator is used to integrate the decision information of multiple stages,which not only retains the powerful advantages of the traditional PRSRV method,but also comprehensively considers the subjective and objective weights’ preferences of the decision maker.Finally,we construct the financial risk assessment classification indicators,and apply the PRSRV method to the financial risk assessment of new energy vehicle companies for providing the company with useful decision-making suggestions.Experiments show that it has stronger data adaptability and can effectively avoid counter-intuitive phenomena caused by aggregation operators and the inconsistency of types in the decision-making process.(6)Research on the q-rung orthopair fuzzy set pair analysis multi-criteria group decision-making method based on MARCOSWe systematically propose the q-rung orthopair fuzzy set pair analysis model,which effectively connects q-rung orthopair fuzzy sets and set pair analysis through connection numbers.It can more objectively and quantitatively describe the uncertainty and certainty of decision-making,and further the basic operations are defined,and the basic framework and conversion conditions are constructed.Furthermore,the connection number distance measure and score function based on the circumcenter point are proposed.In addition,the objective weight determination method based on IOCW and the combined weight determination method of nonlinear combined subjective weight and objective weight are designed,and a q-rung orthopair fuzzy set pair analysis MARCOS(Measurement of Alternatives and Ranking based on COMpromise Solution)multi-criteria group decision making(MCGDM)framework with unknown objective weight and combined weight is established.In the early stage of this method,the modified q-rung orthopair fuzzy aggregation operator is used to integrate the preference information of multiple experts,which not only retains the powerful advantages of the traditional MARCOS method,but also comprehensively considers the subjective and objective weight preferences of decision makers.Finally,in view of the fact that the evaluation value in the cache placement policy evaluation process does not have a unified and standardized measurement,which results in low data credibility and does not comprehensively reflect the pros and cons of the cache placement policy,the linguistic term-q-rung orthopair fuzzy number correspondence table is introduced to reduce decision-making’s difficulty given by the evaluation value of the decision-makers and improve the comprehensive reflection ability of the cache placement policy selection.Meanwhile,we construct the content-centric networking(CCN)cache placement policy evaluation system,and apply the MARCOS method to CCN cache placement policy selection.Experiments show that it has stronger data adaptability and can effectively avoid counter-intuitive phenomena in the decision-making process.